T. Cooper

Micromechanical model for comminution and granular flow of brittle material under high strain rate application to penetration of ceramic targets

Abstract Under sufficiently energetic attack by penetrators or explosives, brittle materials are comminuted and forced into large strain divergent flow, deforming non-elastically by sliding and ride-up of fragments, with accompanying competition between dilatancy and pore compaction. This paper describes a micromechanical model of such deformation with application to penetration of thick ceramic targets. The model was used in parametric finite element code calculations of the penetration of an eroding, long tungsten rod into a target package consisting of a thick aluminum nitride plate confined in steel. The calculations successfully exhibited the key generic features commonly observed experimentally, including the formation of a comminuted ceramic region around the eroding penetrator nose, dilatant expansion of comminuted material into the region behind the penetrator, and conical fractures radiating outward from this region into the intact material. The most important ceramic properties that govern the depth of penetration were inferred to be the friction between comminuted granules, the unconfined compressive strength of the intact material and the compaction strength of the comminuted material. However, further work is needed to define the relative importance of the properties of the comminuted and intact material.

Shape control of large lightweight mirrors with dielectric elastomer actuation

Space-based astronomy and remote sensing systems would benefit from extremely large aperture mirrors that can permit greater-resolution images. To be cost effective and practical, such optical systems must be lightweight and capable of deployment from highly compacted stowed configurations. Such gossamer mirror structures are likely to be very flexible and therefore present challenges in achieving and maintaining the required optically precise shape. Active control based on dielectric elastomers was evaluated in order to address these challenges. Dielectric elastomers offer potential advantages over other candidate actuation technologies including high elastic strain, low power dissipation, tolerance of the space environment, and ease of commercial fabrication into large sheets. The basic functional element of dielectric elastomer actuation is a thin polymer film coated on both sides by a compliant electrode material. When voltage is applied between electrodes, a compressive force squeezes the film, causing it to expand in area. We have explored both material survivability issues and candidate designs of adaptive structures that incorporate dielectric elastomer actuation. Experimental testing has shown the operation of silicone-based actuator layers over a temperature range of -100 °C to 260 °C, suitable for most earth orbits. Analytical (finite element) and experimental methods suggested that dielectric elastomers can produce the necessary shape change when laminated to the back of a flexible mirror or incorporated into an inflatable mirror. Interferometric measurements verified the ability to effect controllable shape changes less than the wavelength of light. In an alternative design, discrete polymer actuators were shown to be able to control the position of a rigid mirror segment with a sensitivity of 1800 nm/V, suggesting that sub-wavelength position control is feasible. While initial results are promising, numerous technical challenges remain to be addressed, including the development of shape control algorithms, the fabrication of optically smooth reflective coatings, consideration of dynamic effects such as vibration, methods of addressing large-numbers of active areas, and stowability and deployment schemes.

A microstatistical model for ductile fracture with rate effects

Abstract A micromechanical ductile fracture model was used in a parametric study of void-induced softening. The model describes rate-dependent nucleation and growth of microscopic void size distributions. The Gurson yield surface is used as the threshold condition for viscous void growth. The relative amounts of shear stress and mean stress relaxations due to void nucleation and growth in a material element are found to be strongly dependent on both the material viscosity and the path taken by the material element in stress space. Material elements subjected to uniaxial stress load paths show much less shear strength softening than those subjected to uniaxial strain load paths. Shear strength softening is enhanced by loading rates high enough to activate viscous response. Computational simulations of uniaxial stress and strain tests over a range of strain rate show a complicated interplay of the above factors.

Model for hot spots in porous frictional material

“Hot spots” can form in materials exposed to penetrating radiation at heterogeneities with higher absorption cross sections than the matrix material, or in materials that contain reactive heterogeneities that become initiated by shock waves. This paper presents a two phase “effective stress” model for cases in which the matrix material is both porous and frictional. The porosity is divided into empty pores and pores containing a second phase material that is preferentially heated and may melt or vaporize. Tension in the matrix material produces time dependent fracture as cracks nucleate and grow to intersection. Example calculations show complex interactions between hot spot size, pressures, and stress waves in the matrix.

Modeling the Flow of Fragmented, Brittle Material

In prior papers [1,2], we presented a granulated material model called FRAGBED for use in finite element “hydrocodes” applied to penetration of ceramic armors. It is a nonlocal, multiplane plasticity model (see, for example, Batdorf and Budianski [3], Curran et al [4], Bazant et al [5,6]). FRAGBED proved to be useful in computational simulations and associated interpretations of penetration experiments in which ceramic armors were attacked by long rod penetrators [2].

A MICROMECHANICAL MODEL FOR GRANULAR MATERIAL AND APPLICATION TO PENETRATION OF CERAMIC ARMOR

Ceramics and brittle geologic materials can deform nonelastically under compression and shear by sliding and ride-up of fragments, grains, or blocks, with accompanying competition between dilatancy and pore compaction. This paper describes a micromechanical model of such deformation based on an analogy to the dynamics of atomic dislocations and using the slipping processes in a multiple-plane plasticity model. In the analogy, atomic lattice slip planes are replaced by slip on interfaces between blocks, and atoms are replaced by fragments, grains, or blocks. The model treats intact material, a gradual transition to fragments, and then the behavior of the fragments. The coefficient of friction between the grains (tan Ψ = 0.11) was determined for aluminum nitride through simulations of a pressure-shear impact experiment. The calibrated model was then used with a finite-element computation of the penetration of a long tungsten rod into an aluminum nitride target The calculations successfully exhibited the key features observed experimentally, such as the rubblized zone just ahead of the penetrator and the dilatant rebound of the ceramic behind the penetrator. The most important microscopic material property governing depth of penetration was found to be the friction between granules in the rubble ahead of the penetrator.